Related papers: Evaluation of binomial series with harmonic number…

In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving…

In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which…

We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…

A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.

A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…

The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series which involves a product of Riemann zeta-functions of a special form.

We evaluate in closed form several series involving products of Cauchy numbers with other special numbers (harmonic, skew-harmonic, hyperharmonic, and central binomial). Similar results are obtained with series involving Stirling numbers of…

Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are given involving sequences of special numbers: Harmonic…

We give a new method for the evaluation of a class of integrals of rational symmetric functions in N pairs of variables {x_a, y_a}_{a=1,... N} arising in coupled matrix models, valid for a broad class of two-variable measures. The result is…

Many authors have recently studied the degenerate harmonic numbers. This paper makes two main contributions. First, we derive several explicit expressions for these numbers, which are a degenerate version of the ordinary harmonic numbers.…

We define bilateral series related to Ramanujan-like series for $1/\pi^2$. Then, we conjecture a property of them and give some applications.

Spivey presented a new approach to evaluate combinatorial sums by using finite differences. We present some closed forms for sums involving the binomial coefficients, Fibonacci and Lucas numbers in terms of the falling factorial.

In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.

Let $\pi:(E,\nabla^{E}) \to (M,g)$ be an affine submersion with horizontal distribution, where $\nabla^{E}$ is a symmetric connection and $M$ is a Riemannian manifold. Let $\sigma$ be a section of $\pi$, namely, $\pi \circ \sigma = Id_{M}$.…

In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.

Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several…

We take advantage of the combinatorial interpretations of many sequences of polynomials of binomial type to define a sequence of symmetric functions corresponding to each sequence of polynomials of binomial type. We derive many of the…

We define an S function as the sum of the asymptotic error terms of digamma function of an arithmetic series, $S(a) \equiv \sum_{n=1}^\infty \left[\ln\frac{n}{a} - \frac{a}{2n}-\psi\left(\frac{n}{a}\right)\right]$, and show a few properties…

We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for subharmonic functions. We also obtain integral inequalities…